A wheel accelerates from rest to 59 rad/s at a rate of 58 rad/s^2 What is the angular displacement of the wheel???
A) 24 rad
B) 38 rad
C) 30 rad
To find the angular displacement of the wheel, we can use the equation:
ω^2 = ω0^2 + 2αθ
Where:
ω is the final angular velocity (59 rad/s),
ω0 is the initial angular velocity (0 rad/s),
α is the angular acceleration (58 rad/s^2), and
θ is the angular displacement (what we need to find).
Rearranging the equation to solve for θ, we have:
θ = (ω^2 - ω0^2) / (2α)
Substituting the given values, we have:
θ = (59^2 - 0^2) / (2 * 58)
θ = (3481) / (116)
θ ≈ 30 rad
Therefore, the angular displacement of the wheel is approximately 30 rad. So the correct answer is C) 30 rad.